Grade 6 · Equations
Ticket model: Undo an unknown's operations
Ticket model investigation: undo an unknown's operations. Change the quantities, follow the motion, and explain the result using the displayed mathematical relationship.
Predict what will happen, press Play, then pause and explain what changed. Every control also works without playback.
Watch the relationship
PausedHD animation studio
From experiment to screen.
Present a crisp Canvas scene, save a full-HD image, or capture your model as a silent video.
Understand what you are seeing
The idea behind the motion.
Solving an equation finds an input that makes two expressions equal. Subtracting the same constant from both sides and dividing both sides by the same nonzero coefficient preserve the solution set. Substitution in the original equation checks the result. This investigation begins with coefficient a = 3; constant b = -3; right side c = 16. Treat the named setting as a constructed classroom model, then explain which relationships would still hold if its numbers changed.
A relationship to keep
ax + b = c → ax = c−b → x = (c−b)/a
Read the symbols alongside the explanation. A diagram shows the relationship; the assumptions tell you when it applies.
- STEP 1
Represent the given quantities
Read the entire original equation, including the sign of the constant term.
- STEP 2
Follow the changing model
Playback first subtracts b from both sides and then divides both sides by a. Each stage preserves equality.
- STEP 3
Check and explain the relationship
Substitute the proposed x into ax+b and verify that the output is exactly c.
Your turn to explain
Make a prediction. Test your reasoning.
Ticket model: Solve 3x + (-3) = 16.
Use the values specified in the question. Reset restores the initial values for this investigation.
Compare your explanation
x = 6.333; substituting gives 16 = 16.
Work through a full lesson
Connect the animation to a worked example and practice questions.